Part III begins twenty days, plus travel time from Liege to Paris, after the end of Part II.  (Chapter XVI: "… every day of the twenty that were spent since his return.")  Unless Caron's entire trip to Antwerp took at most five days including travel time, this means that Part III undoubtedly begins in March, not later than March 21 plus travel time from Liege to Paris.  It doesn't last more than a few days (Chapter XXII: "…why didn't you listen to me when, days ago, I counselled flight?", spoken the penultimate day of the novel) and hence probably also ends in March.

It might be possible to nail down the calendar of Part III by determining the exact date of the execution of the ci-devant Vicomte Anatole d'Ombreval, possibly through research into the family papers of his great-great-grandfather Nicolas Ravot d'Ombreval.